David Cameron has become the first prime minister for more than three decades to visit Shetland as he campaigned against independence on the eve of the Commonwealth Games.

He offered the island a pre-referendum sweetener in the form of continued help with energy bills as he met residents at the town hall and pub in Lerwick, the capital.

Not since Margaret Thatcher visited in 1980 have the islands, which lie more than 100 miles off the mainland, received a prime minister. Edward Heath also visited in the Seventies.

Mr Cameron said he wanted to visit because he cared "passionately" about the future of the Union. "I want us to vote to stay together on Sept 18 and I wanted to come to this, the most far-flung part of our United Kingdom, to listen to people, to hear their concerns and to give the message that I hope we stay together," he said.

During a short speech on Tuesday night, Mr Cameron apologised that it had taken 34 years for a prime minister to return and thanked Shetland for boosting the UK economy through its oil and fish industries.

Mr Cameron followed his speech by heading to a pub in Lerwick. On Wednesday morning he tweeted a picture of himself petting a Shetland pony alongside two children who were holidaying on the island.

Shetland has become something of a thorn in the side of Alex Salmond's push for independence in recent months. Alongside islanders from Orkney and the Outer Hebrides, some Shetlanders have proposed a referendum on splitting away from Scotland in the event of a "yes" vote.

Mr Cameron used the visit to announce an extension to a subsidy that helps keep energy bills low in Shetland. The cost of the subsidy will be spread across the whole of the UK, rather than just northern Scotland.

No10 estimated that the move will keep prices at 75 per cent less than they otherwise would be and lower the average domestic bill by £1,200.

Following his Shetland visit, Mr Cameron will attend a business conference linked to the Commonwealth Games in Glasgow.

Addressing business leaders, he will say the Games are a "fantastic platform" to promote new business for the whole of the UK, evoking the economic legacy of London 2012 Olympics.

The London Games have created an "economic boost" of more than £14 billion in the past two years, higher than a previous target of £11 billion over four years, he will say. The money has come from new business contracts, extra sales and more foreign investment that followed a series of government-backed events held at Lancaster House in London during the Olympics.

Mr Cameron will say there is no reason the feat cannot be repeated. "Part of our long-term economic plan is about promoting every part of our country to the world and Glasgow's Commonwealth Games will give us another fantastic platform to do this," the Prime Minister is expected to say.

Mr Cameron will add that the Coalition will fight for businesses across the UK to "drum up trade, encourage investment and pave the way for growth" to help create a "brighter future for our country".

"I am confident we can build on our experience in London and make Glasgow 2014 so much more than just an amazing sporting event," Mr Cameron will say.

The Prime Minister is also expected to announce new trade and investment deals worth more than £200 million.

Politicians on all sides of the independence debate are understood to be keen to avoid politicising the Commonwealth Games, with the vote less than two months away.